Simplify the following expression: $ z = \dfrac{-3}{9y - 3} - 5 $
Answer: In order to add expressions, they must have a common denominator. Multiply the second expression by $\dfrac{9y - 3}{9y - 3}$ $ \dfrac{-5}{1} \times \dfrac{9y - 3}{9y - 3} = \dfrac{-45y + 15}{9y - 3} $ Therefore $ z = \dfrac{-3}{9y - 3} + \dfrac{-45y + 15}{9y - 3} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{-3 - 45y + 15}{9y - 3} $ $z = \dfrac{-45y + 12}{9y - 3}$ Simplify the expression by dividing the numerator and denominator by 3: $z = \dfrac{-15y + 4}{3y - 1}$